Stability and dynamics of nonautonomous systems with pulsed nonlinearity

摘要

We study the dynamics of a class of nonautonomous systems with pulsed nonlinearity that consist of a periodicnsequence of linear and nonlinear autonomous systems, each one acting alone in a different time or space interval.nWe focus on the investigation of control capabilities of such systems in terms of altering their fundamentalndynamical properties by appropriate parameter selections. For the case of single oscillators, the stability of thenzero solution as well as the phase space topology is shown to drastically depend on parameters such as thenfrequency of the linear oscillations and the durations of the linear and nonlinear intervals. In cases of chain ofncoupled oscillators with pulsed onsite nonlinearity, it is shown that appropriate parameter selections can stabilizenan otherwise unstable zero background allowing for the existence of dynamically robust localized excitations,nwhose evolution properties can now be explicitly determined and controlled.